PUZZLE #3685: Spacetime Causality Cipher (diff 6)

spacetime-causality learn difficulty: 6/7 simulate author: system unsolved

Gravitational waves are ripples in spacetime itself, predicted by Einstein in 1916 and directly detected in 2015 by LIGO.

DATA

Events	`{'label': 'r', 'x': -1, 't': 2}, {'label': 's', 'x': 1, 't': 23}, {'label': 'a', 'x': 0, 't': 13}, {'label': 'F', 'x': -8, 't': 1}, {'label': 'g', 'x': 0, 't': 0}, {'label': 'U', 'x': -2, 't': 1}, {'label': 'S', 'x': -6, 't': 3}, {'label': 'v', 'x': -2, 't': 8}, {'label': 'e', 'x': 2, 't': 19}, {'label': 'v', 'x': 1, 't': 16}, {'label': 'a', 'x': -2, 't': 6}, {'label': 'X', 'x': 11, 't': 3}, {'label': 'w', 'x': -1, 't': 11}`
Speed Of Light	`1`
Hint	`Spacetime diagram: 9 of 13 events are in the future light cone of (0,0). An event (x, t) is causally connected if \|x\| ≤ c·t where c=1. Filter out spacelike events (\|x\| > t), sort remaining by t. GPS satellites use this same physics to maintain cm-level accuracy.`
Answer Format	`lowercase word (the causally connected message)`

{
  "type": "spacetime-causality",
  "events": [
    {
      "label": "r",
      "x": -1,
      "t": 2
    },
    {
      "label": "s",
      "x": 1,
      "t": 23
    },
    {
      "label": "a",
      "x": 0,
      "t": 13
    },
    {
      "label": "F",
      "x": -8,
      "t": 1
    },
    {
      "label": "g",
      "x": 0,
      "t": 0
    },
    {
      "label": "U",
      "x": -2,
      "t": 1
    },
    {
      "label": "S",
      "x": -6,
      "t": 3
    },
    {
      "label": "v",
      "x": -2,
      "t": 8
    },
    {
      "label": "e",
      "x": 2,
      "t": 19
    },
    {
      "label": "v",
      "x": 1,
      "t": 16
    },
    {
      "label": "a",
      "x": -2,
      "t": 6
    },
    {
      "label": "X",
      "x": 11,
      "t": 3
    },
    {
      "label": "w",
      "x": -1,
      "t": 11
    }
  ],
  "speed_of_light": 1,
  "note": "9 causally connected events + 4 spacelike events (noise). Sort by time after filtering.",
  "hint": "Spacetime diagram: 9 of 13 events are in the future light cone of (0,0). An event (x, t) is causally connected if |x| \u2264 c\u00b7t where c=1. Filter out spacelike events (|x| > t), sort remaining by t. GPS satellites use this same physics to maintain cm-level accuracy.",
  "answer_format": "lowercase word (the causally connected message)"
}

author's note: Pool fill: spacetime-causality diff 6